A burner apparatus comprising: a housing having an outlet end and an air discharge section; and a burner wall, which is positioned at the outlet end of the housing and has a longitudinal axis, the burner wall having a forward end, wherein said burner wall surrounds an air flow passageway which extends through said burner wall, said air flow passageway has a forward discharge opening at said forward end of said burner wall, and said burner wall has a longitudinal axis which extends through said air flow passageway and said burner apparatus having within said air discharge section of said housing and within said air flow passageway surrounded by said burner wall only one combustion fuel discharge tip assembly, wherein said combustion fuel discharge tip assembly extends through said air discharge section of said housing and into said air flow passageway of said burner wall, said combustion fuel discharge tip assembly comprises a single combustion fuel discharge tip having a forward end, wherein said forward end of said combustion fuel discharge tip is located at or proximate to said forward discharge opening of said air flow passageway of said burner wall and said combustion fuel discharge tip assembly further comprises a flame stabilizing structure located at, forwardly of, or rearwardly of said forward end of said combustion fuel discharge tip, wherein said combustion fuel discharge tip is located laterally outward with respect to said longitudinal axis of said burner wall in a first lateral half of said air flow passage way of said burner wall between said longitudinal axis and a first interior side of said burner wall to form a non-symmetrical burner such that a combustion fuel ejected from said fuel discharge tip creates side-by-side fuel rich and lean combustion zones which comprise (i) a fuel rich combustion zone located adjacent to said first interior side of said burner wall and (ii) a lean combustion zone located adjacent to a second interior side of said burner wall opposite said first interior side of said burner wall, characterized in that said burner apparatus further comprises a pilot burner assembly which also extends through said air discharge section of said housing into said air flow passageway of said burner wall for initiating combustion at said forward end of said fuel discharge tip; wherein said flame stabilizing structure is a stabilization cone, and at least 90% of a diameter of said stabilization cone is located in said first lateral half of said air flow passageway between said longitudinal axis of said burner wall and said first interior side of said burner wall. a housing having an outlet end and an air discharge section; and a burner wall, which is positioned at the outlet end of the housing and has a longitudinal axis, the burner wall having a forward end, wherein said burner wall surrounds an air flow passageway which extends through said burner wall, said air flow passageway has a forward discharge opening at said forward end of said burner wall, and said burner wall has a longitudinal axis which extends through said air flow passageway and said burner wall surrounds an air flow passageway which extends through said burner wall, said air flow passageway has a forward discharge opening at said forward end of said burner wall, and said burner wall has a longitudinal axis which extends through said air flow passageway and said burner apparatus having within said air discharge section of said housing and within said air flow passageway surrounded by said burner wall only one combustion fuel discharge tip assembly, wherein said combustion fuel discharge tip assembly extends through said air discharge section of said housing and into said air flow passageway of said burner wall, said combustion fuel discharge tip assembly comprises a single combustion fuel discharge tip having a forward end, wherein said forward end of said combustion fuel discharge tip is located at or proximate to said forward discharge opening of said air flow passageway of said burner wall and said combustion fuel discharge tip assembly further comprises a flame stabilizing structure located at, forwardly of, or rearwardly of said forward end of said combustion fuel discharge tip, wherein said combustion fuel discharge tip is located laterally outward with respect to said longitudinal axis of said burner wall in a first lateral half of said air flow passage way of said burner wall between said longitudinal axis and a first interior side of said burner wall to form a non-symmetrical burner such that a combustion fuel ejected from said fuel discharge tip creates side-by-side fuel rich and lean combustion zones which comprise (i) a fuel rich combustion zone located adjacent to said first interior side of said burner wall and (ii) a lean combustion zone located adjacent to a second interior side of said burner wall opposite said first interior side of said burner wall, characterized in that said burner apparatus further comprises a pilot burner assembly which also extends through said air discharge section of said housing into said air flow passageway of said burner wall for initiating combustion at said forward end of said fuel discharge tip; wherein said flame stabilizing structure is a stabilization cone, and at least 90% of a diameter of said stabilization cone is located in said first lateral half of said air flow passageway between said longitudinal axis of said burner wall and said first interior side of said burner wall.